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Question
On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?
Solution
Let the number of children be x and the amount distributed by Seema for one child be ₹ y.
So, (x - 8)(y + 10) = xy
⇒ 5x - 4y = 40 ....(i)
and
(x + 16)(y - 10) = xy
⇒ 5x - 8y = - 80 ...(ii)
To solve (i) and (ii),
let A = `((5,4),(5,-8)), "B" = ((40),(-80)), "X" = (("x"),("y"))`
∵ `"AX" = "B" ⇒ "X" = "A"^-1 "B"`
Now `"A"^-1`
`"A^-1 = - 1/20 ((-8,4),(-5, 5))`
⇒ `(("x"),("y")) = ((32),(30))`
Clearly x = 32, y = 30.
Hence the number of children = 32 and the amount distributed by Seema = ₹ 30.
Value reflected: Helpfulness towards the needy people.
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